相关论文: On the existence of flips

This paper investigates the short-time existence and uniqueness of Ricci flow solutions on Finsler manifolds. The main results of this paper are theorems demonstrating the short-time existence of the flow solution for $n$-dimensional…

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

Congruence between two n-point sets in 4 dimension can be checked in O(n log n) time. On the way to establishing this result, we revisit several parts of 4-dimensional geometry, such as angles and distances between planes, Hopf fibrations,…

This work is devoted to the proof of the statement about the existence of palindromic continued fractions in an arbitrary dimension. In addition, it is proved the criterion that an algebraic continued fraction has proper cyclic palindromic…

We study etale extensions of rings that have FIP.

Given a matching between n red points and n blue points by line segments in the plane, we consider the problem of obtaining a crossing-free matching through flip operations that replace two crossing segments by two non-crossing ones. We…

A flip is a minimal move between two triangulations of a polytope. An open question is whether any two triangulations of the product of two simplices can be connected through a series of flips. This was proven in the case where one of the…

We study degree one maps between closed orientable 4-manifolds with cyclic $\pi_1$, and obtain some results on the existence and finiteness, as well as some relation of $1$-domination and Euler Characteristics.

We prove that for all $n$, simultaneously, we can choose prime filtrations of $R/I^n$ such that the set of primes appearing in these filtrations is finite.

We prove, using a fixed point theorem in a Banach algebra, an existence result for a fractional functional differential equation in the Riemann-Liouville sense. Dependence of solutions with respect to initial data and an uniqueness result…

We give a short, elementary and explicit proof of the existence of Hilbert schemes of points on affine schemes. As a direct consequence we obtain the existence of the Hilbert scheme of points on any projective scheme, not necessarily of…

We consider zigzags in thin complexes. The main result states that the sum of the lengths of all zigzags in an $n$-complexe is equal to the sum of the lengths of all zigzags in all $(n-1)$-faces of this complex, and this sum also is the…

We systematically introduce and study a new type of singularities, namely, exceptionally non-canonical (enc) singularities. This class of singularities plays an important role in the study of many questions in birational geometry, and has…

For a finite dimensional algebra $A$ with $0 < \phi dim (A) = m < \infty$ we prove that there always exist modules $M$ and $N$ such that $\phi(M) = m-1$ and $\phi (N) = 1$. On the other hand, we see an example of an algebra that not every…

This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…

We first prove that the set of domino tilings of a fixed finite figure is a distributive lattice, even in the case when the figure has holes. We then give a geometrical interpretation of the order given by this lattice, using (not…

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

In this note we observe that the categorical structure of a flop occurs for some well-known non-commutative resolutions of a nodal curve. We describe the flop-flop spherical twists, and give a geometric interpretation in terms of…

A necessary and sufficient condition is given for the existence of an embedding of an irreducible subshift of finite type into the Fibonacci-Dyck shift

We establish the existence, finiteness, and uniqueness up to scaling of various isoperimetric profiles of a group, in all dimensions. We also show that these profiles all coincide in dimensions 4 and higher; in particular, the nth Dehn…